Of the light generated by an LED device, only the light that escapes the device is usable for illumination purposes. To increase the amount of light that escapes the device, and correspondingly to decrease the amount of light that is reflected back into the device and absorbed, certain surfaces of the LED device may be roughened. For example, in a commercial laterally-contacted LED device the p-type gallium nitride (p-GaN) layer on the top of the LED device is sometimes grown such that its upper surface is rough. Due to this roughening, more of the light generated within the active layer of the LED device will pass through the upper surface of the p-GaN layer and escape the device. There are also other ways of increasing the amount of light that escapes an LED device. For example, the epitaxial gallium-nitride layers of an LED device are grown on a substrate. Rather than this substrate having a smooth upper surface, the upper surface upon which the epitaxial layers are grown can be roughened. The resulting roughness of the substrate-to-epi interface at the bottom of the LED device promotes light extraction. Although these methods of increasing light extraction function quite well, they also have certain drawbacks in certain circumstances. For example, an LED whose p-GaN layer is grown to be rough may exhibit an undesirably high forward voltage and may suffer from reliability problems under high voltage conditions. Manufacturing costs associated with an LED whose epitaxial layers are grown on a roughened sapphire substrate may be undesirably high due to the expense of obtaining machine-roughened wafers.